Reduced complexity dynamic spectrum management based on a polar coordinates formulation

This paper deals with the problem of power allocation in a multi-user, multicarrier communication system. This problem arises, for example, in wireless OFDM or digital subscriber line networks. Users transmitting concurrently on the same sub-carriers cause interference to each other, and this interference is a serious limitation for system performance. We consider the problem of maximizing the weighted sum of users' data rates. The optimization variables are vectors containing the powers for all users on each tone. The problem is intrinsically difficult due to the non-concavity of the utility function. We propose to change the (cartesian) power vector by its polar coordinates vector equivalent. The main contribution of this paper is to show that at least for one dimension of the polar coordinates vector, the radius, the problem is concave and thus easy to solve. We develop an algorithm based in such a polar coordinates formulation to exploit such concavity. It is demonstrated that the algorithm we propose saves considerably on computational cost compared to previous algorithms.